Faculty of Cognitive Sciences and Human
Development
COOPERATIVE LEARNING: NUMBERED HEADS TOGETHER `S
STRATEGY IN LEARNING MATHEMATICS AMONG SECONDARY
SCHOOL STUDENTS
A CASE STUDY
NORZUBAIDAH BINTI AB.HALIN
Bachelor of Education (Mathematics)
with Honours
2009
COOPERATIVE LEARNING: NUMBERED HEADS TOGETHER `S
STRATEGY IN LEARNING MATHEMATICS AMONG SECONDARY
SCHOOL STUDENTS
A CASE STUDY
NORZUBAIDAH BINTI AB.HALIN
This project is submitted in partial fulfilment of the requirements for the
degree of Bachelor of Education (Honours) Mathematics
Faculty of Cognitive Sciences and Human Development
UNIVERSITI MALAYSIA SARAWAK
2009
This project entitled “Cooperative Learning: Numbered Heads Together `s
Strategy in Learning Mathematics among Secondary School Students. A Case
Study” was prepared by Norzubaidah Binti Ab.Halin and submitted to the Faculty
of Cognitive Sciences and Human Development in partial fulfilment of the
requirements for a Bachelor of Education (Honours) Mathematics.
Received for examination by:
-------------------------------------------(Tuan Haji Suaidi Bin Haji Otek)
Date:
--------------------------
Grade
Statement of Originality
The work described in this Final Year Project, entitled
"Cooperative Learning: Numbered Heads Together `S Strategy In Learning Mathematics Among
Secondary School Students.A Case Study
is to the best of the author’s knowledge that of the author except
where due reference is made.
__________________
___________________
(Date submitted)
Norzubaidah Bt Ab.Halin
14879
i
ACKNOWLEDGEMENT
Bismillahhirrahmanirrahim.
Assalamualaikum w.b.t.
All praises and thanks to God the Almighty for giving me strength, confidence
and enthusiasm in my study and complication of my graduation project.
Alhamdulillah, finally the project that had been struggled to complete came to it
end.
This project would not have been possible without the guidance and the help of
many great people. Special thanks to my supervisor, Tuan Haji Suaidi Bin Haji
Otek, for his tireless guidance, advice and support throughout the duration of this
project.
Finally, special acknowledgement is expressed to my beloved father and mother,
Ab.Halin Bin Wan Ahmed and Norizan Binti Omar, my siblings and friends,
whose love, understanding, encouragement and support helped me through in
some of the difficult moments in conducting the research and study at UNIMAS.
May God bless all of you, Amin.
ii
TABLE OF CONTENTS
i
ii
iii
vi
vii
viii
ix
Statement of Originality
Acknowledgement
Table of Contents
List of Tables
List of Figures
Abstract
Abstrak
CHAPTER 1 INTRODUCTION
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
Introduction
Background
Research problem
Objectives of the study
1.3.1 General Objective
1.3.2 Specific Objective
Research Questions
Rational of the study
Conceptual Framework
Significance of the study
Limitation of the study
Conceptual and Operational Definitions of Terms
1.9.1 Cooperative learning
1.9.2 Numbered Heads Together
Conclusion
1
3
5
7
7
7
8
8
9
10
11
11
12
12
13
CHAPTER 2 LITERATURE REVIEW
2.0
2.1
2.2
2.3
2.4
2.5
2.6
Introduction
Definition of Cooperative Learning
Models of Cooperative Learning
2.2.1 Numbered Heads Together
Historical Foundation, Theoretical and Empirical Support
of Cooperative Learning
2.3.1 Cognitive Development Theories
2.3.2 Constructivism
2.2.3 Social Learning Theory
Advantages of Cooperative Learning
2.4.1 Advantages of Numbered Heads Together `s
strategy In Learning Mathematics
Disadvantages of Cooperative Learning
2.5.1 Disadvantages of Numbered Heads Together
In Learning Mathematics
Effectiveness of Numbered Heads Together In Learning
Mathematics
iii
14
15
16
17
19
20
21
22
23
25
26
27
28
2.7
Conclusion
29
CHAPTER 3 METHODOLOGY
3.0
3.1
3.2
3.3
3.4
Introduction
Research Design
Location of Research
Sampling
Instruments of Research
3.4.1 Semi-structured interview
3.4.1.1 The Development and Description of SemiStructured Interview
3.4.2 Self-reflection Inventory
Procedure of Data Collection
Procedure of Data Analysis
Conclusion
3.5
3.6
3.7
30
30
31
31
33
33
34
36
36
37
40
CHAPTER 4 FINDING AND DISCUSSION
4.0
4.1
4.2
4.3
Introduction
Findings
4.1.1 Part A : Semi-Structured Interview
4.1.1.1 Section A
4.1.1.2 Section B
4.1.2 Part B: Self-reflection Inventory
Discussion of Research Findings
4.2.1 Advantages of Cooperative Learning by Using
Numbered Heads Together `s strategy in Learning
Mathematics.
4.2.2 Disadvantages of Cooperative Learning by Using
Numbered Heads Together `s strategy in Learning
Mathematics.
4.2.3 Effectiveness of Cooperative Learning by Using
Numbered Heads Together `s strategy in Learning
Mathematics.
Conclusion
CHAPTER 5
5.0
5.1
5.2
5.3
5.4
5.5
CONCLUSION AND RECOMMENDATIONS
Introduction
Summary of the study
Summary of the findings
Implications of the research
Suggestions for the further research
Conclusion
41
42
42
42
44
56
62
62
64
65
66
68
68
70
71
72
73
74
80
References
Appendices
iv
LIST OF TABLES
Table 2.1
Four Steps In Numbered Heads Together` s Strategy In Cooperative
Learning
18
Table 3.1
Procedure of Data Analysis
38
The table 4.1
Sample quotation (I)
43
The table 4.2
Sample quotation (II)
44
The table 4.3
Sample quotation (III)
45
The table 4.4
Sample quotation (IV)
46
The table 4.5
Sample quotation (V)
47
The table 4.6
Sample quotation (VI)
48
The table 4.7
Sample quotation (VII)
48
The table 4.8
Sample quotation (VIII)
50
The table 4.9
Sample quotation (IX)
53
The table 4.10
Sample quotation (X)
54
The table 4.11
Sample quotation (XI)
54
The table 4.12
Sample quotation (XII)
55
v
The table 4.13
Sample quotation (XIII)
56
The table 4.14
Percentage of advantages of cooperative learning by using Numbered
Heads Together `s strategy.
58
The table 4.15
Percentage of disadvantages of cooperative learning by using Numbered
Heads Together `s strategy.
59
The table 4.16
Percentage of effectiveness of cooperative learning by using Numbered
Heads Together `s strategy.
60
The table 4.17
Sample quotation (XIV)
61
The table 4.18
Sample quotation (XV)
62
vi
LIST OF FIGURE
Figure 1.1
Conceptual framework
9
Figure 3.1
The Procedures of Sampling.
33
vii
ABSTRACT
COOPERATIVE LEARNING: NUMBERED HEADS TOGETHER `S
STRATEGY IN LEARNING MATHEMATICS AMONG SECONDARY
SCHOOL STUDENTS
A CASE STUDY
Norzubaidah Binti Ab.Halin
This study aims to identify the use of cooperative learning by using Numbered
Heads Together` strategy in learning Mathematics among secondary school
students. The use of cooperative learning via this strategy was analyzed in terms
of advantages (positive interdependence, individual accountability, equal
participation and simultaneous interaction), disadvantages (time consuming,
ineffective if students have poor social skill and encourage bad behavior) and
effectiveness of this learning approach. These three criteria were chosen base on
the framework identified by Spencer Kagan on 1992 (Waugh, 2003), Smaldino et
al (2005), Bellanca & Fogarty (2003) and Johnson & Johnson (2004). In the
attempt of data collection, the researcher carried out six experiments of
cooperative learning via this strategy among From Two and From Four students in
a secondary school at Kuching, Sarawak. Semi-structured interview and selfreflection inventory forms were used as instruments of this research. Based upon
their academic achievement in Mathematics subject, a number of twenty
respondents were interviewed. This process was recorded using tape recorder. The
data were transcribed and later analyzed according to research questions. The
finding indicated that most of the respondents believe the advantages of
cooperative learning by using this strategy are positive interdependence,
individual accountability, equal participation and simultaneous interaction.
However, a minority of respondents claim that disadvantages of this strategy are
time consuming, ineffective if students have poor social skill and encourage bad
behavior. The result also showed that this strategy is an effective way of learning
Mathematics among secondary schools. Finally, the researcher has come out
successfully with views of cooperative learning by applying Numbered Heads
Together `s strategy in learning Mathematics.
viii
ABSTRAK
PEMBELAJARAN KOPERATIF: KAEDAH ‘NUMBERED HEADS
TOGETHER’ DALAM MEMPELAJARI MATEMATIK DI KALANGAN
PELAJAR SEKOLAH MENENGAH.
SATU KAJIAN KES.
Norzubaidah Binti Ab.Halin
Kajian ini bertujuan untuk mengenalpasti kegunaan pembelajaran koperatif
dengan menggunakan kaedah ‘Numbered Heads Together’ dalam mempelajari
Matematik dikalangan pelajar sekolah menengah. Kegunaan pembelajaran
koperatif melalui kaedah ini di analisis mengikut kebaikan kaedah (saling
membina, bertanggungjawab, penyertaan yang sama rata dan komunikasi yang
serentak), keburukan kaedah (masa yang tidak dapat dikawal, tidak berkesan
apabila diapplikasikan kepada pelajar yang mempunyai tahap pergaulan yang
rendah dan menggalakan perangai buruk) dan keberkesanan kaedah ini. Ketigatiga kreteria tersebut telah dikenalpasti berdasarkan kepada Spencer Kagan pada
1992 (Waugh, 2003), Smaldino et al (2005), Bellanca & Fogarty (2003) dan
Johnson & Johnson (2004). Bagi prosedur pengumpulan data, pengkaji telah
menjalankan enam eksperimen tentang pembelajaran koperatif melalui kaedah ini
dikalangan pelajar Tingkatan Dua dan Empat di sebuah sekolah di Kuching
,Sarawak. Sesi temubual separa berstruktur dan borang kajiselidik digunakan
sebagai alat kajian. Berdasarkan pencapaian akademik terdahulu subject
Matematik, dua puluh pelajar telah ditemubual. Kesuluruhan proses
pengumpulan data ini direkodkan menggunakan parakam suara. Data yang telah
direkodkan akan ditranskrip seterusnya di analisis mengikut soalan kajian. Hasil
kajian menunjukan bahawa kebanyakan responden mempersetujui kebaikan
pembelajaran koperatif adalah saling membina, bertanggungjawab, penyertaan
yang sama rata dan komunikasi yang serentak. Namun, hanya segelintir
responden mempercayai keburukan pembelajaran koperatif ialah masa yang tidak
dapat dikawal, tidak berkesan apabila diapplikasikan kepada pelajar yang
mempunyai tahap pergaulan yang rendah dan mengalakan perangai buruk. Hasil
kajian juga menunjukan bahawa kaedah ini adalah satu kaedah yang berkesan
untuk mempelajari subject Matematik di kalangan pelajar sekolah menengah.
Akhirnya, pengkaji berjaya menghasilkan satu pandangan/pendapat tentang
penggunaan pembelajaran koperatif melalui ‘Numbered Heads Together`
dikalangan pelajar sekolah menengah.
ix
CHAPTER 1
INTRODUCTION
1.0
Introduction
This chapter discusses about the background of the study, research
problem, objectives of the study, research questions, rationale of the study,
conceptual framework, significance of the study, limitation of the study,
conceptual and operational definitions of terms and conclusion.
In Mathematics, teachers play many roles such as making decision related
to what to teach, what teaching materials to use and the best method to teach the
selected content (Moore, 2003). The days of teacher standing in front of the room,
giving lecture for 40 minutes and then assigning exercises in the text book are no
longer effective for today`s students. Beside that, drill and practice is no longer an
effective approach that can be applied on a daily basis with an expectancy of
1
excellent when it relates to Mathematical problem solving and deeply
understanding of Mathematical concept. According to Macnab & Payne (2003),
secondary school Mathematics becomes boring and difficult compared with the
primary school. A Mathematics teacher should find an effective way to make
learning process more meaningful.
According to Sutton & Krueger (2002, as cited in Cline, 2007), learning is
an active process that allows students the opportunity to create understanding
through empirical investigation and group interaction. Hanson & Silver (1996 as
cited in Cline, 2007) claim that students should understand what they learn, make
the connection that Mathematics is real and apply it to daily life. They recommend
that Mathematics should provide challenging task and interesting where students
can be actively involved. Cline (2007) states that cooperative learning actively
involved students with other students in the classroom. This gives them an
opportunity to demonstrate and use the knowledge they have learned. According
to Moore (2003), teachers must manage a classroom environment. Thus, teachers
are environmental engineers who organize the classroom space to fit their learning
goals and to maximize learning. Moore (2003) also states that an emerging
approach of grouping which is proving effective learning at both the elementary
and secondary level is cooperative learning.
Generally, cooperative learning involves mixed-ability students work
together to accomplish a set of task and achieve the learning`s goals. Besides that,
Moore (2003) claims that rewards to individual student are usually based on the
performance and achievement of the whole team rather than on that of individual
team members, which provided motivation for students to work together
productively. On other hand, Coronel, Carrasco, Fernandez & Gozalez (2003)
state that in cooperation, the basic unit of learning is the group rather than the
individual learner. This shift in the axis on which the work turns requires the
concurrence of the principles such as moral support, increased capacity for
reflection and continues improvement (Coronel et al, 2003)
2
Cooperative learning method promoted individual needs and interests in a
group environment (Davidson & Kroll, 1991 as cited in Bosfied, 2004). Besides
that, Arends (1997) said that cooperative learning developed to achieve at least
three instructional goals which are academic achievement, acceptance of diversity
and social skill development. Numbered Heads Together is one of the best
strategies which can be applied in teaching Mathematics’ concept (Kagan, 1994).
A teacher can focus on one strategy of cooperative learning in teaching process to
stimulate meaningful lesson.
1.1
Background
Mathematics is a very important subject and there have been a continuing
controversy over Mathematics learning process, mostly in the computation skills.
According to Cline (2007), build student’s capacity for Mathematical thinking,
there must be Mathematical communication. Sutton & Kruger (2002, as cited in
Cline, 2007), claim that all students can learn Mathematics and all students need
to learn Mathematics. Mathematic anxiety is a problem for many people. It can
have harmful effects on students including feelings of stress, nervous and tension
(Truttschel, 2002). Furthermore, the type of language used by teacher also
effected student` s understanding of Mathematical concepts. There are many
factors that contribute to students’ Mathematical achievement such as understand
the student`s differences in learning styles and needs, foster communication and
develop a safe learning community.
According to Cline (2007), the Institute for Dynamic Educational
Advancement (2006) reported that cooperative learning is an offshoot of
constructivism. Bosfield (2004) claims the cooperative learning method was
created in the late 1700s by Joseph Lancaster. Lancaster developed an
apprenticeship system in which students get a lot of advantages from helping each
other (Bosfield, 2004). Besides that, according to Kagan (1994), cooperative
learning is a successful teaching method in which small teams, each student with
different levels of ability and use a variety of learning activities to improve their
3
understanding of a subject. Kagan (1994 as cited in Cline,2007) stated that
cooperative hard work result in participants motivated for sharing advantages so
that all the students in a small group will gain from each other`s efforts, “your
success benefits me and my success benefits you”. Besides, each of the students,
know that one's performance is equally caused by oneself and one's team
members, “We can not do it without you”. They also know that all group
members share a common chance and feel proud and jointly celebrate when a
group member achievement the success.
According to Lo (1991 as cited in Bosfield, 2004), educators of
Mathematic in the 1980s make changes at teaching methods because students are
unable to apply Mathematics to everyday experiences. In addition, Bosfield
(2004) states that in 1993, a national report compiled by National Assessment of
Education Progress found that students accomplish basic Mathematics
computation in their examination, but were not able to apply Mathematics to
everyday experiences. Boaler (1998 as cited in Bosfield, 2004) states that current
study shows that teacher - centered learning method (traditional approach) places
more emphasis on procedural knowledge that is of limited use rather than on
understanding, thinking and reasoning.
The concept of constructivism is learning by doing which is related to
cooperative learning. According to Kauchack & Eggen (2003), constructivists
view learning as an active process in which the learners actively construct
knowledge as they try to understand what is being experienced and the techniques
involved. Besides that, constructivists believe students need to be participating
fully in their learning. Harris & Graham, (1994 as cited in Kauchack & Eggen,
1994) said that participating fully will lead to deep, real, rich understanding and
use of knowledge which will in turn guide to the ability to apply what is learned.
Kauchack & Eggen (1994) also said that other theories which are related
with cooperative learning are Bruner in 1973 and Vygotsky in 1978. The idea of
Bruner and Vygotsky is that learning happens most successfully when students
4
are actively engaged, working together, drawing from previous personal
experiences to construct new knowledge and seeking to accomplish shared goals.
According to Kagan (1994), there are many cooperative learning`s strategy
which are Numbered Heads Together, Turn To Your Neighbor or Think-PairShare, Pairs of Pairs, Inside-Outside Circle, Co-Op, T-Chart and Teams-Games
Tournament. Kagan (1994) believes that each cooperative learning`s strategy has
its own unique purpose and goal. The structure of Numbered Heads Together is
derived from the work of Spencer Kagan (Bellanca & Fogarty, 2003). Since 1967,
Kagan has focused his research on the structural approach to cooperative learning
(Bellanca & Fogarty, 2003). There are four steps in Numbered Heads Together `s
strategy which is numbering, questioning, head together and answering (Arends,
1997).
In the globalization world, the students should know how to apply the
Mathematics concept in everyday experiences and it is necessary to use an
effective teaching approach in order to lead a better understanding of
Mathematics` s concept and higher achievement.
1.2
Research problem
Learning Mathematics involves remembering a lot of facts but also
understanding the various concepts. In fact, not all students in one class have
excellent ability in calculating and solving Mathematical problem. According to
Lo (1991 as cited in Bosfield), since the 1980s, students have been lacking in the
ability to apply Mathematical concepts to everyday life and teachers have felt the
pressure to make changes in order to overcome this problem. In addition, the
students feel bored and worried while working on Mathematics task. Mathematics
anxiety is an extremely common phenomenon among students today (Perry,
2004). Mathematics anxiety is a problem. It can influence students’ academic
achievement and even contribute to stress, which is well known to cause many
other problems (Truttschel, 2002).
5
Furthermore, the student`s performance and achievement in Mathematics
when teaching in second language, English has shown an alarming decrease as
measured state tests, report cards and daily and weekly assessments. This problem
has an impact to the school, community and student`s futures. Secondary school
students are expected to know basic mathematics’ concept and apply the concept
in multiple questions correctly. Due to students’ lack of vocabulary knowledge
and basic skill, the task of completing the question is extremely difficult. There
are many possible factors that contribute to this problem such as direct instruction
is only being the teaching style utilized, lack of practices and lack of knowledge
among teachers in orientation to best practices in Mathematics.
In other to improve the student`s achievement in Mathematics, changes is
needed. According to Cline (2007), ‘insanity is doing the same thing over and
over and expecting a different result’. He claims that, it is logical to consider that
changes in teaching practices may have better results in student`s achievement
especially in Mathematics. Bosfield (2004) believes that cooperative learning
stimulates higher achievement compared to teacher- centered method. The
increased usage of the cooperative learning method is a visible change within the
area of learning Mathematics (Davidson & Kroll, 1991 as cited in Cline, 2007).
Numbered Heads Together is one of cooperative learning which can be applied in
teaching Mathematics’ concept effectively (Gaikwad, 1996). In Number Heads
Together `s strategy, students are given time and procedures for analyzing how
their learning functions (Gaikwad, 1996). He also states that, the strategy not only
focused on content that needs to be mastered but also the social skills that assist
all group members to maintain effective working relationship within the group.
Teaching Mathematics involves creating, maintaining, enriching and
adapting instruction to move towards Mathematical learning goals, capture and
maintain interest and engage students in building Mathematical understanding.
Cline (2007) claims that Kagan `s research on cooperative learning suggest that if
cooperative learning is applied to the teaching of Mathematics, students`
6
Mathematics achievement might increase. The computation and the ability to
analyze mathematical problems are important to their future education and in the
work place. Therefore, this case study was carried out to solve this problem by
investigating the use of Numbered Heads Together `s strategy in learning
Mathematics among secondary school students.
1.3
Objectives of the study
The purposes of this study were to:
1.3.1
General Objective:
To study the use of cooperative learning which is Numbered Heads
Together `s strategy in learning Mathematics among secondary school students.
1.3.2
i.
Specific Objective:
To find out the advantages of cooperative learning by using Numbered
Heads Together `s strategy in learning Mathematics among secondary
school students.
ii.
To find out the disadvantages of cooperative learning by using Numbered
Heads Together `s strategy in learning Mathematics among secondary
school students.
iii.
To identify the effectiveness by applying cooperative learning which is
Numbered Heads Together` s strategy in learning Mathematics among
secondary school students.
7
1.4
Research Questions
The research questions were as follows:
i.
What are the advantages of cooperative learning by using Numbered
Heads Together `s strategy in learning Mathematics among secondary
school students?
ii.
What are the disadvantages of cooperative learning by using Numbered
Heads Together `s strategy in learning Mathematics among secondary
school students?
iii.
What is the effectiveness by applying cooperative learning which is
Numbered Heads Together `s strategy in learning Mathematics among
secondary school students?
1.5
Rational of the study
The study of Numbered Heads Together’s strategy was chosen because
this strategy has high tendency to improve students` achievement more than
traditional approaches (Johnson and Johnson, 2004). In addition, this strategy is
suitable to apply in the teaching-learning process since it doesn`t consume much
time. Mathematics is an uneasy subject to master by students. Therefore, a teacher
needs to apply a helpful strategy in learning process. According to Johnson,
Johnson & Holubec (1988 as cited in Gaikwad,1996), the main benefits of
cooperative learning identified by the extensive studies are higher achievement,
increased retention, greater use of higher level reasoning strategies, increased
critical reasoning competencies and more positive attitudes toward subject areas.
The design of this study was qualitative in order to develop a views of Numbered
Heads Together` s strategy though interviews and self-reflection inventory .This
techniques gave more meaningful and honesty feedback because it directly ask the
respondents.
8
1.6
Conceptual Framework
Problems statement: Mathematics anxiety is a problem faced by secondary school
students. Furthermore, learning Mathematics in English language has been
effected student`s achievement. The method of teaching and learning Mathematics
should be improved. The researcher investigated Cooperative Learning`s method
which is Numbered Heads Together` strategy in order to find an effective way to
learn Mathematics.
Research Question
Research Question
Research Question
I
II
III
(Objective 1)
(Objective 1)
(Objective 1)
Data were collected by using methods of semi-structured interview and selfinventory Form
The relevant data was chosen by researcher
The researcher organizes the data based on to its
Analyzing
respective questions
stage in
descriptive
The relevant inferences were quoted in order to
support the finding of the research.
and statistic
form
Views of cooperative learning by using Numbered Heads Together `s strategy in
learning Mathematics among secondary school students
Figure 1.1: Conceptual Framework
Figure 1.1: Conceptual framework
9
In this study, the respondents were from Forms Two and Four students in a
secondary school at Kuching, Sarawak interviewed by researcher based on three
research questions. The respondents also filled in the self-inventory form to
support the finding. The data was collected represent the use of cooperative
learning by using Numbered Head Together `s strategy in learning Mathematics
among secondary school students. The collected data analyze in descriptive and
statistic form. As the result from this study, views of cooperative learning by
using Numbered Head Together’s strategy in learning Mathematics among
secondary school students was obtained.
1.7
Significance of the study
This study investigated the use of cooperative learning which is Number
Head Together `s strategy in learning Mathematics among secondary school
students. It is hoped that the study will provide important research relating to
Mathematical achievement. Beside that, this is an academic area that is lacking
research. The study was an effort to assist and guide the students’ success in
Mathematics especially among secondary school students. A teacher should use
effective teaching methods that can help students and offer opportunities to learn
in good environment that is nonthreatening and stimulating. This is very essential
to unsure that the learning objective will achieve successfully. This study was
value to teachers and administrators. The administrators can apply the result from
this study to encourage Mathematics teachers at secondary school to use this
learning strategy.
It is also hoped that the result of this study would present an elevated
understanding of cooperative learning in teaching-learning Mathematics.
According to Cruickshank, Jenkins and Metcalf (2003), cooperative learning is an
effective strategy to create teams of musketeers who come to one another`s
assistance and who succeed together no matter what the circumstances. This
research brought relevant information needed for the transition period in
Mathematical learning. Furthermore, the study investigated and focus on the
10
effectiveness Numbered Heads Together` s strategy which is one of the
cooperative learning approaches. Thus, this study was valuable for future teacher
training and development.
1.8
Limitation of the study
Since this study was conducted among Form Two and Form Four students,
the range of age was limited to 14 and 16 years old only. The results would vary if
this study was done by focusing on bigger age range such as adult group (19-23
years old). Besides that, the limitation of this study was the research was done in
only one school in Sarawak which was located at rural area. The result of this
study also would differ if the study was carried out at other secondary schools in
Sarawak, town area and Malaysia at large.
Another limitation of the study was the research focused only on the
academic area of Mathematic s’ subject and selected respondents among
secondary school students in a school. The findings of this study would different
if were used bigger range of respondents and another subjects. In addition,
interview technique that was used to collect data influenced the respondents to
answer the question only based on the questions asked to them and some
respondents not give full cooperation with the researcher. Besides that, the
researcher has not enough time to collect all the data regarding to the study since
time is limited.
1.9
Conceptual and Operational Definitions of Terms
The following terms was being defined to avoid confusion:
11
1.9.1
Cooperative learning
Conceptual definition terms:
A teaching arrangement that refer to small, heterogeneous groups of students
working together to achieve a learning objectives. Students work together to learn
and are responsible to their teammates (Kagan, 1994 as cited in Cline, 2007).
According to Cline (2007), cooperative learning defines as a structured systematic
instructional strategy in which small groups work together toward a common goal.
Operational definition:
Cooperative learning refer to teaching approach whereby the students working
together to achieve a learning objectives in teaching and learning Mathematics
among secondary school students in a secondary school in Kuching, Sarawak.
1.9.2
Numbered Heads Together.
Conceptual definition:
Numbered Heads Together is a strategy of cooperative learning developed by
Spencer Kagan (1993) to involve more students in the review of materials covered
in a lesson and check their understanding of a lesson`s content based on four steps
which are numbering, questioning, head together and answering (Arends, 1997).
Operational definition:
Numbered Heads Together is a strategy of cooperative learning applied in
teaching and learning Mathematics among secondary school to involve more
students in the review of materials covered in a lesson and check their
understanding of a lesson`s content based on four steps which are numbering,
questioning, head together and answering
12